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Basic ideas
Published in C.W. Evans, Engineering Mathematics, 2019
It must be stressed that these properties are not self-evident and in fact require quite advanced mathematics to put them on a rigorous footing. Nevertheless we shall be content, for the moment, to apply them and we conclude this chapter by giving a practical application.
Historical overview on the development of converter steelmaking from Bessemer to modern practices and future outlook
Published in Mineral Processing and Extractive Metallurgy, 2019
A comparison between the OBM and BOP processes reveals clear differences; bottom blowing leads to near-to-equilibrium results, whereas after top blowing the slag and the metal bath both are significantly over-oxidised. The reason is self-evident: bottom blowing induces intensive stirring and good mixing, whereas top blown oxygen jet has weaker and relatively local stirring effect leaving the most of the steel bath quite quiescent. On the other hand, bottom blowing represents a more complicated technique, with extra expense and risk, compared to lance blowing. Hence, the combination of the benefits of both processes into one seemed optimal. Numerous combined processes arose since the middle 1970s to 1980s. Most of these were based on the LD process with additional inert gas bottom blowing. Today, a great majority of converters are such hybrid processes. The estimated stirring effect of the bottom gas for different processes is illustrated in Figure 5, where mixing time is presented as a function of bottom gas flow rate (Chatterjee et al. 1984).
Accounting for the variability of lecturing practices in situations of concept introduction
Published in International Journal of Mathematical Education in Science and Technology, 2022
On one occasion, the expected utility of examples did not only differ from one teacher to the other, they also ran opposite to one another. Teachers B and F endeavoured to help students make sense of the formal definition by studying a worked example, but B studied sequences (with technical proofs using absolute values and the algebra of inequalities), whereas C studied (with a two-line proof based on the Archimedean property of ). Not only did B and C own their behaviours; they also evaluated the other alternative negatively. C first acknowledged that studying could be worth it, yet time consuming and better suited for one of the exercise-classes. She then elaborated on her choice of , thus implicitly criticizing B’s choice: examples should be ‘the simplest, just to see how the definition is used, with no other difficulty which might blur the message’. By contrast, when prompted to comment on C’s use of to illustrate the definition of convergence, B defended his choice of : ‘I don’t want to do something too commonplace. (…) is so self-evident to them [students] so … why bother?’ F’s reading of C’s choice of was also rather negative, but for a reason almost oppositive to B’s: He politely expressed doubt that something so ‘advanced’ as the Archimedean property could be illuminating for students.
A physical effort-based model for pedestrian movement in topographic urban environments
Published in Journal of Urban Design, 2020
Eliyahu Greenberg, Asya Natapov, Dafna Fisher-Gewirtzman
In order to assess the performance of the PEM, it was compared to the other two axial segment models described above: The topological model and the angular model. All models go through the first stage of the PEM (redrawing segments according to topography) so the comparison is only between the analysis modes. The reason it is important for a cognitive model based on mutual visibility to have its lines actually represent lines of sight is self-evident and hard to argue against. The second stage of the model is much more open to scrutiny and therefore is the one to be evaluated.